Realistic Colored Fur?
I managed to figure it out on my own.  Basically I needed to do less desaturation than I was doing on the fur, and apply more (as opposed to none) desaturation to the underlying skin.  That, and also doubling (and then clamping) the brightness of the transmission color.

This .blend contains the tweaks I did to fix it up: http://www.pasteall.org/blend/36094

And below is a render of the fixed shader.  Probably not 100% realistic, but it's better.